Active Gizmo show all even when axis locked
You have changed the orientation for the gizmo. Locking the global X,Y-axes will cause the X,Y-axes to be hidden in the gizmo only if the gizmo is set to global or default orientation.

The setting for this is found in the top left of your screen. Do not confuse the Gizmo Orientation with Transform Orientation. The transform orientation (middle of screen) is used as the when you use a hotkey such as G to edit an object.